This paper develops a continuous functional framework for treatment effects that propagate through geographic space and economic networks. We derive a master equation governing propagation from three economic foundations -- heterogeneous agent aggregation, market equilibrium, and cost minimization -- establishing that the framework rests on fundamental principles rather than ad hoc specifications. A key result shows that the spatial-network interaction coefficient equals the mutual information between geographic and market coordinates. The Feynman-Kac representation decomposes effects into inherited and accumulated components along stochastic paths representing economic linkages. The framework nests the no-spillover case as a testable restriction. Monte Carlo simulations demonstrate that conventional estimators -- two-way fixed effects, difference-in-differences, and generalized propensity score -- exhibit 25-38% bias and severe undercoverage when spillovers exist, while our estimator maintains correct inference regardless of whether spillovers are present. Applying the framework to U.S. minimum wage policy, we reject the no-spillover null and find total effects at state borders four times larger than direct effects -- conventional methods capture only one-quarter of policy impact. Structural estimates reveal spatial diffusion consistent with commuting-distance labor mobility, network diffusion consistent with quarterly supply chain adjustment, and significant spatial-network interaction reflecting geographic clustering of industries. Entropy-based fragility diagnostics outperform standard centrality measures by 56-76% in predicting labor market disruptions, identifying all high-risk state-industry pairs during 2020-2021 with six-month advance warning.

翻译：本文构建了一个连续函数框架，用于分析通过地理空间和经济网络传播的处理效应。我们从三个经济学基础——异质性主体加总、市场均衡与成本最小化——推导出描述传播过程的主方程，表明该框架建立在基本原理而非特定设定之上。一个关键结果表明，空间-网络交互系数等于地理坐标与市场坐标之间的互信息。基于Feynman-Kac表示，效应可分解为沿代表经济关联的随机路径上的继承分量与累积分量。该框架将无溢出情形作为可检验约束纳入其中。蒙特卡洛模拟表明，当存在溢出效应时，传统估计方法（双向固定效应、双重差分法、广义倾向得分）会产生25-38%的偏误及严重的覆盖不足，而我们的估计量无论是否存在溢出均能保持正确的统计推断。将该框架应用于美国最低工资政策分析，我们拒绝了无溢出效应的原假设，发现州边界处的总效应是直接效应的四倍——传统方法仅能捕捉政策影响的四分之一。结构估计显示：空间扩散与通勤距离劳动力流动性一致，网络扩散与季度供应链调整一致，显著的空间-网络交互则反映了产业的地理集聚性。基于熵的脆弱性诊断指标在预测劳动力市场扰动方面优于标准中心性指标56-76%，能在2020-2021年间对全部高风险州-产业组合提前六个月发出预警。